The present invention relates to multicylinder internal-combustion engines of the type comprising:                at least one intake valve and at least one exhaust valve for each cylinder, each valve being provided with respective elastic return means, which push the valve towards a closed position for controlling respective intake and exhaust pipes; and        at least one camshaft, for actuating the intake and exhaust valves of the engine cylinders by means of respective tappets;        in which each intake valve is controlled by the respective tappet against the action of the aforesaid elastic return means by interposition of hydraulic means that include a pressurized fluid chamber;        said pressurized fluid chamber being designed to be connected by means of a solenoid valve to an exhaust channel in order to uncouple the valve from the respective tappet and bring about fast closing of the valve as a result of the respective elastic return means;        electronic control means for controlling each solenoid valve so as to vary the time and the opening stroke of the respective intake valve according to one or more operating parameters of the engine;        in which associated to each intake or exhaust valve is a control piston slidably mounted in a guide bushing;        in which said control piston faces a chamber with variable volume communicating with the pressurized-fluid chamber both via first communication means controlled by a non-return valve, which enables only passage of fluid from the pressurized-fluid chamber to the variable-volume chamber, and via second communication means, which enable passage of fluid between the two chambers in both directions;        said device further comprising hydraulic-braking means designed to cause a restriction of said second communication means in the final phase of closing of the valve of the engine.        
An engine of the type specified above is, for example, described and illustrated in the European patent application EP-A-0 803 642 in the name of the present applicant.